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The Atmospheric Energy Moisture Balance Model

The energy-moisture balance climate model we employ is based upon the vertically integrated energy-moisture balance equations, in which advection terms are replaced by an eddy-diffusive approximation, over the oceans, the energy balance (in ice-free and ice covered regions), is expressed by,
displaymath2337
over land we assume no heat or moisture storage, and hence we write
displaymath2339
where tex2html_wrap_inline2341 is a constant surface air density, tex2html_wrap_inline2343 the specific heat capacity of air, tex2html_wrap_inline2345 a constant scale height depth representative of the atmosphere, and tex2html_wrap_inline2347 the surface air temperature. The terms on the right hand side of (2.1.1) are the various sources/sinks of heat into/out of the system. Here
displaymath2349
is the eddy-diffusive horizontal heat transport parameterization, in which tex2html_wrap_inline2351 is the longitude, tex2html_wrap_inline2353 is the latitude, a is the radius of the earth, and tex2html_wrap_inline2357 is a latitudinally dependent heat transport coefficient.

In general, the atmosphere may absorb upwards of 30 % of the total incoming shortwave radiation through the combined effects of water vapour, dust, ozone and clouds (Ramanathan, 1987). To mimic these effects, we apply a source term in the atmosphere:
displaymath2359
where tex2html_wrap_inline2361 is the solar constant, S is the annual distribution of heat flux entering the top of the atmosphere (North, 1975), tex2html_wrap_inline2365 is the albedo, and tex2html_wrap_inline2367 is a reduction parameter representing the scattering/absorption processes described above. Over land, all shortwave radiation intercepted is assumed returned (via black body radiation) to the atmosphere so that tex2html_wrap_inline2369 assumes a value of zero there.

The net longwave relaxation to space is modeled by considering the planet as a grey body with emissivity tex2html_wrap_inline2371. The infrared emission is then given by
displaymath2373
where tex2html_wrap_inline2375 is the Stefan-Boltzmann constant. Alternatively the moisture longwave feedback effect can be taken into account by employing the planetary longwave parameterization of Thompson and Warren (1982).
displaymath2377
where tex2html_wrap_inline2379, r is the relative humidity, and tex2html_wrap_inline2381 are empirically derived constants (see Thompson and Warren, 1982, Table 3).

The longwave radiation emitted by the ocean is strongly absorbed by greenhouse gases present in the atmosphere. The atmosphere then re-emits this absorbed energy both upward and downward resulting in a longwave flux at the base of the atmosphere, which we model as a grey body emission. The radiative flux is written as
displaymath2383
where tex2html_wrap_inline2385 is the sea, and ice surface temperature, respectively; and tex2html_wrap2327 are the oceanic, ice, and atmospheric emissivities.

A traditional bulk parameterization is utilized for the sensible heat flux:
displaymath2387
where tex2html_wrap_inline2389 is the Stanton number, and U is the surface scalar wind speed. The latent heat flux into the atmosphere takes the form
displaymath2393
where tex2html_wrap_inline2395 is the latent heat of evaporation, syr is the number of seconds in a year, and P is the precipitation (in meters per year - assumed to occur when saturation exceeds 85 %).

A moisture balance equation has also been added so that the atmospheric hydrological cycle can be included. We obtain a parameterization of the hydrological cycle by considering an approximation to the balance equation for water vapor in the atmosphere. In this approximation we replace the horizontal advection terms by an eddy diffusive term. Vertically integrating over the depth of the atmosphere we obtain
displaymath2401
where tex2html_wrap2328 is a constant scale height depth for the specific humidity, tex2html_wrap_inline2403, tex2html_wrap2329 is an eddy diffusive horizontal redistribution term, P is the precipitation, and E is the evaporation (ablation over ice is neglected in the moisture source terms, but retained in the ice heat budget). The evaporation is calculated from its traditional bulk formula
displaymath2409
where tex2html_wrap_inline2411 is the Dalton number, tex2html_wrap_inline2413 is the saturation specific humidity at tex2html_wrap_inline2415 (calculated by appealing to the Clausius-Clapeyron equation and utilizing the empirical formula of Bolton, 1980):
displaymath2417
Traditionally, a constant humidity is used in the bulk parameterization for the evaporation (e.g. Haney, 1971), however, since we also consider the conservation of water vapor, this is not necessary in the present formulation.

To obtain closure of (2.1.8) we parameterize the precipitation as
displaymath2419
where tex2html_wrap_inline2421 is the model time step, tex2html_wrap2330 is the saturation specific humidity at tex2html_wrap_inline2347, r is the relative humidity, and
displaymath2427


next up previous contents
Next: The Ice Model Up: Modeling the Climate System Previous: Modeling the Climate System

Daniel Robitaille
Mon May 5 14:22:13 PDT 1997